Question

How do you prove `tan² x(1 + cot² x) = sec² x`?

Answer 1

Consider that:
`tanx=sinx/cosx`
`cotx=cosx/sinx`
`secx=1/(cosx)`
So you get:
`sin^2x/cos^2x(1+cos^2x/(sin^2x))=1/cos^2x`
`cancel(sin^2x)/cancel(cos^2x)((sin^2x+cos^2x)/cancel(sin^2x))=1/cancel(cos^2x)`
And: `sin^2x+cos^2x=1`